Robust Strategies for Automated AFM Force Curve Analysis—II: Adhesion-Influenced Indentation of Soft, Elastic Materials

2007 ◽  
Vol 129 (6) ◽  
pp. 904-912 ◽  
Author(s):  
David C. Lin ◽  
Emilios K. Dimitriadis ◽  
Ferenc Horkay
Keyword(s):  
Young’S Modulus ◽  
Young's Modulus ◽  
Full Range ◽  
Soft Materials ◽  
Adhesive Contact ◽  
Colloid Interface ◽  
Inhomogeneous Materials ◽  
Dugdale Model ◽  
Normal Contact ◽  
Adhesive Interactions

In the first of this two-part discourse on the extraction of elastic properties from atomic force microscopy (AFM) data, a scheme for automating the analysis of force-distance curves was introduced and experimentally validated for the Hertzian (i.e., linearly elastic and noninteractive probe-sample pairs) indentation of soft, inhomogeneous materials. In the presence of probe-sample adhesive interactions, which are common especially during retraction of the rigid tip from soft materials, the Hertzian models are no longer adequate. A number of theories (e.g., Johnson–Kendall–Roberts and Derjaguin–Muller–Toporov), covering the full range of sample compliance relative to adhesive force and tip radius, are available for analysis of such data. We incorporated Pietrement and Troyon’s approximation (2000, “General Equations Describing Elastic Indentation Depth and Normal Contact Stiffness Versus Load,” J. Colloid Interface Sci., 226(1), pp. 166–171) of the Maugis–Dugdale model into the automated procedure. The scheme developed for the processing of Hertzian data was extended to allow for adhesive contact by applying the Pietrement–Troyon equation. Retraction force-displacement data from the indentation of polyvinyl alcohol gels were processed using the customized software. Many of the retraction curves exhibited strong adhesive interactions that were absent in extension. We compared the values of Young’s modulus extracted from the retraction data to the values obtained from the extension data and from macroscopic uniaxial compression tests. Application of adhesive contact models and the automated scheme to the retraction curves yielded average values of Young’s modulus close to those obtained with Hertzian models for the extension curves. The Pietrement–Troyon equation provided a good fit to the data as indicated by small values of the mean-square error. The Maugis–Dugdale theory is capable of accurately modeling adhesive contact between a rigid spherical indenter and a soft, elastic sample. Pietrement and Troyon’s empirical equation greatly simplifies the theory and renders it compatible with the general automation strategies that we developed for Hertzian analysis. Our comprehensive algorithm for automated extraction of Young’s moduli from AFM indentation data has been expanded to recognize the presence of either adhesive or Hertzian behavior and apply the appropriate contact model.

Robust Strategies for Automated AFM Force Curve Analysis—I. Non-adhesive Indentation of Soft, Inhomogeneous Materials

2006 ◽  
Vol 129 (3) ◽  
pp. 430-440 ◽  
Author(s):  
David C. Lin ◽  
Emilios K. Dimitriadis ◽  
Ferenc Horkay
Keyword(s):  
Young’S Modulus ◽  
Elastic Properties ◽  
Large Scale ◽  
Young's Modulus ◽  
Soft Materials ◽  
Data Sets ◽  
Inhomogeneous Materials ◽  
Afm Indentation ◽  
Large Scale Analysis ◽  
Engineered Cartilage

The atomic force microscope (AFM) has found wide applicability as a nanoindentation tool to measure local elastic properties of soft materials. An automated approach to the processing of AFM indentation data, namely, the extraction of Young’s modulus, is essential to realizing the high-throughput potential of the instrument as an elasticity probe for typical soft materials that exhibit inhomogeneity at microscopic scales. This paper focuses on Hertzian analysis techniques, which are applicable to linear elastic indentation. We compiled a series of synergistic strategies into an algorithm that overcomes many of the complications that have previously impeded efforts to automate the fitting of contact mechanics models to indentation data. AFM raster data sets containing up to 1024 individual force-displacement curves and macroscopic compression data were obtained from testing polyvinyl alcohol gels of known composition. Local elastic properties of tissue-engineered cartilage were also measured by the AFM. All AFM data sets were processed using customized software based on the algorithm, and the extracted values of Young’s modulus were compared to those obtained by macroscopic testing. Accuracy of the technique was verified by the good agreement between values of Young’s modulus obtained by AFM and by direct compression of the synthetic gels. Validation of robustness was achieved by successfully fitting the vastly different types of force curves generated from the indentation of tissue-engineered cartilage. For AFM indentation data that are amenable to Hertzian analysis, the method presented here minimizes subjectivity in preprocessing and allows for improved consistency and minimized user intervention. Automated, large-scale analysis of indentation data holds tremendous potential in bioengineering applications, such as high-resolution elasticity mapping of natural and artificial tissues.

scholarly journals Multi-material direct ink writing of photocurable elastomeric foams

2021 ◽  
Vol 2 (1) ◽  
Author(s):  
Osman Dogan Yirmibesoglu ◽  
Leif Erik Simonsen ◽  
Robert Manson ◽  
Joseph Davidson ◽  
Katherine Healy ◽  
...  
Keyword(s):  
Young’S Modulus ◽  
Young's Modulus ◽  
Transient Behavior ◽  
Soft Materials ◽  
Ammonium Bicarbonate ◽  
Structure Property ◽  
Direct Ink Writing ◽  
Material Chemistry ◽  
New Applications ◽  
Double Networks

AbstractDevelopments in additive manufacturing have enabled the fabrication of soft machines that can safely interface with humans, creating new applications in soft robotics, wearable technologies, and haptics. However, designing custom inks for the 3D printing of soft materials with Young’s modulus less than 100 kPa remains a challenge due to highly coupled structure-property-process relationship in polymers. Here, we show a three-stage material chemistry process based on interpenetrating silicone double networks and ammonium bicarbonate particles that decouples the transient behavior during processing from the final properties of the material. Evaporation of ammonium bicarbonate particles at the final stage creates gaseous voids to produce foams with a low effective Young’s modulus in the 25 kPa −90 kPa range. Our photoirradiation-assisted direct ink writing system demonstrates the ability to maintain high resolution while enabling controlled loading of ammonium bicarbonate particles. The resultant multi-material possesses programmed porosity and related properties such as density, stiffness, Shore hardness, and ultimate strength in a monolithic object. Our multi-hardness synthetic hand and self-righting buoyant structure highlight these capabilities.

scholarly journals Influence of Soil Heterogeneity on the Contact Problems in Geotechnical Engineering

2021 ◽  
Vol 11 (9) ◽  
pp. 4240
Author(s):  
Hao Gu ◽  
Kang Liu
Keyword(s):  
Young’S Modulus ◽  
Penalty Method ◽  
Young's Modulus ◽  
Geotechnical Engineering ◽  
Contact Problems ◽  
Soil Heterogeneity ◽  
Contact Forces ◽  
Horizontal Scale ◽  
Normal Contact ◽  
Scale Of Fluctuation

Contact problems are widely encountered in geotechnical engineering, such as the contact between soils and concrete used in earth and rockfill dams, tunnels and coastal levees. Due to the unknown contact region and contact forces, the contact problems have strong boundary nonlinearity. In addition, soils have been recognized as heterogeneous materials in geotechnical engineering. The existence of the soil heterogeneity increases the nonlinearity of the contact problems. Currently, the contact problems are mostly analysed without considering the soil heterogeneity, which may not reflect the contact behavior well. In order to investigate the influence of soil heterogeneity on the contact problems, in this paper, a simple plane-strain contact problem is analysed as an example. In this example, Young’s modulus is taken to be a spatially variable. The local average subdivision (LAS) is used to model the heterogeneity of Young’s modulus. The penalty method is utilised to determine the contact behavior. By the first use of linking the penalty method with the LAS, the proposed approach can be used to analyse the contact problems considering soil heterogeneity. The results show that the influence of soil heterogeneity on the elastic contact problems is significant. The contact forces of the heterogeneous case present apparent variation compared to the results of the homogeneous case. The distribution of the contact force at a specific point is also normal when Young’s modulus is normally distributed, moreover, the coefficient of variation (COV) and the horizontal scale of fluctuation of Young’s modulus affect the extent of variation of the normal contact forces. The standard deviation of the normal contact force increases with the increase of the COV and decreases with the increase of the horizontal scale of fluctuation of Young’s modulus. From the analyses, to better predict the deformation/stress in the contact problems, heterogeneity needs to be considered.

Elasticity and microfibrillar angle in the wood of Sitka spruce

1966 ◽  
Vol 166 (1004) ◽  
pp. 245-272 ◽  
Keyword(s):  
Cell Wall ◽  
Young’S Modulus ◽  
Young's Modulus ◽  
Full Range ◽  
Quadratic Function ◽  
Sitka Spruce ◽  
Cellulose Microfibrils ◽  
Helical Angle ◽  
Microfibrillar Angle ◽  
Experimental Findings

The initial value of Young’s modulus, E , has been measured for small specimens of Sitka spruce wood taken from the annual rings of two disks and has been found in both cases to increase from pith to bark. The decrease from pith to bark in the helical angle θ of the cellulose microfibrils in the walls of the tracheids averaged over an annual ring has been determined from matched specimens. E has been found to vary regularly with θ . Two mathematical models of the cell involved have been developed and the experimental findings applied to the relations derived between E and θ . The first model was that of a number of helical springs free to slip, twist and bend and gave a relationship between the helical angle and the reciprocal of Young’s modulus as proportional to tan 2 θ . The second model, that of an anisotropic homogeneous cell wall, gave 1/ E as being proportional to a quadratic function in sin 2 θ . Relative shear in the cell wall has been predicted from this latter model. The tan 2 θ relation is found to hold provided θ is less than about 40°. The sin 2 θ relation holds, on the other hand, over the full range of θ observed. Some implications of these relations are discussed.

On Effective Mechanical Properties of Two-Dimensional Porous Materials

2020 ◽  
Vol 12 (04) ◽  
pp. 2050040
Author(s):  
Zaoyang Guo ◽  
Lei Wang ◽  
Xiaojun Guo ◽  
Yang Chen ◽  
Leiting Dong
Keyword(s):  
Porous Materials ◽  
Young’S Modulus ◽  
Poisson’S Ratio ◽  
Young's Modulus ◽  
Full Range ◽  
Theoretical Models ◽  
Poisson's Ratio ◽  
Analytical Models ◽  
Two Dimensional ◽  
Effective Mechanical Properties

Two-dimensional (2D) representative volume element (RVE) has been widely used to simulate the effective behaviors of the materials with aligned pores. In this paper, the anisotropy indexes are defined for the 2D RVE model to quantitatively evaluate the extent of anisotropy of the model. A normalized procedure is then proposed to compute the effective moduli of the RVE models, which can further minimize the influence of anisotropy of the RVE models. The effective Poisson’s ratio of the porous materials is challengeable to be estimated well, and few analytical models can give good predictions. The theoretical models are proposed to approach the effective Young’s modulus and the effective Poisson’s ratio of the 2D porous materials covering the full range of porosity. It is numerically validated that the theoretical models give accurate predictions for the effective Young’s modulus and Poisson’s ratio of the 2D porous materials.

scholarly journals Quantitative Visualization of the Nanomechanical Young’s Modulus of Soft Materials by Atomic Force Microscopy

Nanomaterials ◽  
2021 ◽  
Vol 11 (6) ◽  
pp. 1593
Author(s):  
Seongoh Kim ◽  
Yunkyung Lee ◽  
Manhee Lee ◽  
Sangmin An ◽  
Sang-Joon Cho
Keyword(s):  
Young’S Modulus ◽  
Mechanical Characteristics ◽  
Young's Modulus ◽  
Target Surface ◽  
Soft Materials ◽  
Industrial Applications ◽  
Sample Type ◽  
Atomic Force ◽  
Quantitative Visualization ◽  
Tip Radius

The accurate measurement of nanoscale mechanical characteristics is crucial in the emerging field of soft condensed matter for industrial applications. An atomic force microscope (AFM) can be used to conduct nanoscale evaluation of the Young’s modulus on the target surface based on site-specific force spectroscopy. However, there is still a lack of well-organized study about the nanomechanical interpretation model dependence along with cantilever stiffness and radius of the tip apex for the Young’s modulus measurement on the soft materials. Here, we present the fast and accurate measurement of the Young’s modulus of a sample’s entire scan surface using the AFM in a newly developed PinPointTM nanomechanical mode. This approach enables simultaneous measurements of topographical data and forcedistance data at each pixel within the scan area, from which quantitative visualization of the pixel-by-pixel topographical height and Young’s modulus of the entire scan surface was realized. We examined several models of contact mechanics and showed that cantilevers with proper mechanical characteristics such as stiffness and tip radius can be used with the PinPointTM mode to accurately evaluate the Young’s modulus depending on the sample type.

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